Numerical Simulation of Hydraulic Fracture Propagation Guided by Single Radial Boreholes
Abstract
:1. Introduction
2. Establishment of a Fluid-Solid Coupling Mathematical Model and Its Finite Element Discretization
2.1. Stress Balance Equation
2.2. Continuity Equation
2.3. Boundary Conditions
2.4. Finite Element Discretization Method and Stress-Seepage Coupling Equation
3. Numerical Simulation of Propagation of Hydraulic Fracture
3.1. Introduction to the Model
3.1.1. Simulation of Initial Fracture
3.1.2. Level-Set Simulation of Fracture Propagation
3.1.3. Criteria for Initiation of Fracture
3.1.4. Damage Evolution Law
3.1.5. Energy Release Rate Criterion
3.1.6. Solution
3.2. Assumptions
- (1)
- Only a strip of hydraulic fracture is generated during fracturing, which is initiated along the azimuth of the radial borehole [34].
- (2)
- The formation rock is isotropic.
3.3. Fundamental Parameters of Model
4. Analysis of Simulation Results
4.1. Azimuth of Radial Borehole
4.2. Horizontal In-Situ Stress Differences
4.3. Radial Borehole Diameter
4.4. Length of Radial Borehole
4.5. Young’s Modulus of Reservoir Rock
4.6. Poisson’s Ratio of Reservoir Rock
4.7. Reservoir Permeability
4.8. Fracturing Fluid Viscosity
4.9. Fracturing Fluid Injection Rate
4.10. Gray Correlation Analysis of Guidance Factors
5. Experimental Verification
6. Conclusions and Suggestions for Future Work
- (1)
- The influence of in-situ stress could be overcome by scientifically arranging the single radial borehole under certain reservoir conditions, which realizes directional propagation towards target area. Thus, the problem that the hydraulic fracture only propagates along the direction parallel to horizontal maximum in-situ stress, and the available wellbores fail to develop the remaining oil and trap reservoir, and complex multi-fractures tend to generate in the immediate vicinity of wellbore, which makes it hard to realize the deep penetration of fractures, are solved to improve the effectiveness of fracturing operations and recovery efficiency in oil fields.
- (2)
- The concept of ‘guidance factor’ is introduced for the first time to quantify the guidance of a radial borehole on hydraulic fractures. A large amount of simulation shows that the ‘guidance factor’ reflects the guidance of a radial borehole on hydraulic fractures, and larger guidance factor reflects weaker guidance strength.
- (3)
- A smaller radial borehole azimuth, horizontal in-situ stress difference and larger radial borehole diameter and length create stronger guidance strength, and vice versa. When the azimuth of the radial borehole increases from 15°to 45°, the guidance factor increases 2.6 times as much; when the horizontal in-situ stress difference increases from 2 MPa to 8 MPa, the guidance factor increases 3.6 times; when the wellbore diameter increases from 3 cm to 7 cm, the guidance factor decreases 75%; when the well length increases from 10 m to 20 m, the guidance factor decreases 69%.
- (4)
- Both reservoir physical properties and fracturing operation parameters influence the guidance of radial boreholes on hydraulic fractures. The increased Poisson’s ratio and injection rate strengthen the radial borehole guidance, and the increased Young modulus and permeability weaken the radial borehole guidance, both excessive high and low viscosity go against radial borehole guidance of hydraulic fractures, and a fracturing fluid viscosity between 50–100 mPa·s creates the best guidance on propagation of hydraulic fractures.
- (5)
- The gray correlation analysis results show that the influence level (from strong to weak) of the above factors on radial borehole guidance may be listed as follows: horizontal in-situ stress differences > azimuth > borehole diameter > length > fracturing fluid injection rate > Young modulus of rock > reservoir permeability > fracturing fluid viscosity > Poisson’s ratio. The parameters of the radial borehole, physical property parameters of the reservoir and fracturing operation parameters together influence the guidance strength of a radial borehole on hydraulic fractures.
- (6)
- The numerical model is based on real rock parameters from a practical field. It is recommended that the numerical model of different fields and areas should be established based on their rock physical mechanical parameters, and the influence of different factors on guidance be analyzed to obtain radial borehole parameters and fracturing operation parameters applicable to their conditions, which is beneficial to improving the fracturing success rate.
- (7)
- The experimental results show that the guidance of a single radial borehole on hydraulic fracture propagation is limited by the radial borehole azimuth and horizontal in-situ stress difference. A single radial borehole with larger azimuth and larger horizontal in-situ stress difference has poor guidance of the directional propagation of hydraulic fractures. The experimental results are consistent with the numerical simulation results, which shows that the numerical simulation results are reliable to some extent.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Parameters | Value | Parameters | Value |
---|---|---|---|
Reservoir saturation | 1 | Poisson ratio of rock | 0.25 |
Initial pore pressure | 20 MPa | Young’s modulus of rock | 12.9 GPa |
Initial porosity | 0.16 | Reservoir permeability | 60 × 10−3 μm2 |
Horizontal maximum principal stress (σH) | 41 MPa | Filtration coefficient | 10−10 m s−1 |
Horizontal minimal principal stress (σh) | 36 MPa | Injection rate of fracturing fluid | 3.2 m3 min−1 |
Overburden stress | 45 MPa | Fracturing fluid viscosity | 50 mPa·s |
Tensile strength of rock | 3.0 MPa | Fracturing fluid density | 9525 kg/m3 |
Casing diameter | 139.7 mm | Reservoir model size (diameter) | 40 m |
No. | Parameters | Correlation Coefficient |
---|---|---|
1 | Radial well azimuth | 0.7680 |
2 | Radial well diameter | 0.7537 |
3 | Radial well length | 0.7485 |
4 | Horizontal principal stress difference | 0.7921 |
5 | Young’s modulus of rock | 0.7465 |
6 | Poisson ratio of rock | 0.5312 |
7 | Reservoir permeability | 0.7367 |
8 | Fracturing fluid viscosity | 0.7354 |
9 | Injection rate of fracturing fluid | 0.7476 |
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Guo, T.; Qu, Z.; Gong, F.; Wang, X. Numerical Simulation of Hydraulic Fracture Propagation Guided by Single Radial Boreholes. Energies 2017, 10, 1680. https://doi.org/10.3390/en10101680
Guo T, Qu Z, Gong F, Wang X. Numerical Simulation of Hydraulic Fracture Propagation Guided by Single Radial Boreholes. Energies. 2017; 10(10):1680. https://doi.org/10.3390/en10101680
Chicago/Turabian StyleGuo, Tiankui, Zhanqing Qu, Facheng Gong, and Xiaozhi Wang. 2017. "Numerical Simulation of Hydraulic Fracture Propagation Guided by Single Radial Boreholes" Energies 10, no. 10: 1680. https://doi.org/10.3390/en10101680